Finite Group Databasebeta

← C2×#19133555 #25068691

Subgroups — C2×#19133555 #25068691

Order 11008.

1232 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583494C211yesmaximal, characteristic
2C2×#14583055C211yesmaximal, characteristic, complemented
3C2×#14582818C211yesmaximal, characteristic, complemented
4#19133555C218yesmaximal, direct product factor
5C2×#14582637C211yesmaximal, characteristic, complemented
6C2×#14582633C211yesmaximal, characteristic
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#448C211yesmaximal, characteristic
9C22×#10621885—21no—
10#14583494—22no—
11#14583494—22no—
12#14583494—22no—
13#14583494C2214yes—
14C2×#13063318—21no—
15C2×#13063315—21no—
16C2×#13063306—21no—
17C2×#13063306—21no—
18C2×#13063304C2211yescharacteristic
19C2×#13063302—21no—
20C2×D4×Dic43—21no—
21C22×Dic43⋊C4—21no—
22C22×Dic43⋊C4C2211yescharacteristic
23#14583055—22no—
24#14583055C2214yescomplemented
25C2×#13063249—21no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27#14582818—22no—
28#14582818C2214yescomplemented
29C2×C43⋊#95—21no—
30C2×C43⋊#95C2211yescharacteristic
31#14582637C2214yescomplemented
32#14582633C2214yes—
33#14582624C2214yescomplemented
34C23×Q8×C43C2211yescharacteristic
35C22×SD16×C43—21no—
36C2×#121×C43C2211yescharacteristic
37C43×#448—22no—
38C43×#448C2214yes—
39C2×#103×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
41C22×Dic86D411yescharacteristic
42C23×Dic43—21no—
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C23×Dic43D411yescharacteristic
46C2×#10621885—24no—
47C2×#10621885—44no—
48C22×C43⋊C8—21no—
49#13063318—24no—
50#13063318—24no—
51#13063315—24no—
52#13063315—24no—
53#13063306—24no—
54#13063306—24no—
55#13063306—24no—
56#13063306—24no—
57#13063304—21no—
58#13063304—21no—
59#13063304D412yes—
60#13063304C2312yes—
61#13063302—24no—
62#13063302—24no—
63D4×Dic43—24no—
64D4×Dic43—24no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—24no—
75C2×Dic43⋊C4—44no—
76C2×Dic43⋊C4D412yes—
77C2×Dic43⋊C4C2312yes—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83#13063249—24no—
84C22⋊(C43⋊C8)—21no—
85C22⋊(C43⋊C8)C2312yes—
86C43⋊#95—21no—
87C43⋊#95—24no—
88C43⋊#95C2312yes—
89C22×Q8×C43—21no—
90C22×Q8×C43—21no—
91C22×Q8×C43—21no—
92C22×Q8×C43—21no—
93C22×Q8×C43—21no—
94C22×Q8×C43—44no—
95C22×Q8×C43C2312yes—
96C22×D4×C43—21no—
97C22×D4×C43D411yescharacteristic
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100C2×SD16×C43—24no—
101C2×SD16×C43—44no—
102C22×C8×C43—21no—
103#121×C43—21no—
104#121×C43—21no—
105#121×C43D412yes—
106#121×C43C2312yes—
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C22⋊C4×C43—21no—
109#103×C43—24no—
110C22⋊C8×C43—21no—
111C22⋊C8×C43C2312yes—
112C24×C43—21no—
113C24×C43C2×D411yescharacteristic
114C2×Q8×C43—24no—
115C2×Q8×C43—24no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—44no—
119C2×Q8×C43—42no—
120C2×Q8×C43—42no—
121C2×Q8×C43—44no—
122C2×Q8×C43—44no—
123C2×Q8×C43—44no—
124C2×Q8×C43—41no—
125C2×Q8×C43—41no—
126C2×D4×C43—21no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—42no—
130C2×D4×C43—42no—
131C2×D4×C43—42no—
132C2×D4×C43C2×D412yes—
133C22×C4×C43—24no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43—41no—
139C22×C4×C43—41no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—24no—
147C22×Dic43—24no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—82no—
161C22×Dic43C2×D412yes—
162C22×Dic43C2×D412yes—
163C2×Dic86—21no—
164C2×Dic86—42no—
165C2×Dic86C2×D412yes—
166SD16×C43—48no—
167C2×C8×C43—22no—
168C2×C8×C43—42no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×D412yes—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊Dic43—24no—
174C22⋊Dic43—24no—
175C22⋊Dic43—24no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178#10621885—48no—
179C4⋊Dic43—24no—
180C4⋊Dic43—21no—
181C4⋊Dic43C2×D412yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—22no—
190Dic43⋊C4—48no—
191C4×Dic43—24no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—42no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43#12011yescharacteristic
201C23×C43#12011yescharacteristic
202C23×C43#13512yes—
203C23×C43#13712yes—
204C23×C43C22×D411yescharacteristic
205Q8×C43—24no—
206Q8×C43—24no—
207Q8×C43—42no—
208Q8×C43—42no—
209Q8×C43—44no—
210Q8×C43—44no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—44no—
215D4×C43—81no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—24no—
219C2×C4×C43—22no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—44no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—44no—
229C2×C4×C43#12011yescharacteristic
230C2×C4×C43#12011yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×Dic43—24no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—42no—
241C2×Dic43—48no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—81no—
250C2×Dic43—84no—
251Dic86—42no—
252Dic86—81no—
253C8×C43—42no—
254C43⋊C8—42no—
255C2×#1603—431nomaximal, Sylow
256C22×C43—24no—
257C22×C43—24no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—84no—
266C22×C43#45212yes—
267C22×C43#45212yes—
268C22×C43#45612yes—
269C22×C43B(4,𝔽2)12yes—
270C22×C43C2×#12011yescharacteristic
271C22×C43C2×#13511yescharacteristic
272C22×C43C2×#13711yescharacteristic
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—42no—
278C4×C43—44no—
279Dic43—44no—
280Dic43—42no—
281Dic43—42no—
282Dic43—42no—
283Dic43—42no—
284C2×#539—431no—
285C2×#451—431no—
286C2×#448D4311yescharacteristic
287C2×#395—431no—
288#1603—438no—
289C2×#328—431no—
290C2×#327—431no—
291C2×#324—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—22no—
295C2×C43—82no—
296C2×C43#160314yescomplemented
297C2×C43C2×#45211yescharacteristic
298C2×C43C2×#45611yescharacteristic
299C2×C43C2×B(4,𝔽2)11yescharacteristic
300C23×Q8C2×D4311yescharacteristic
301C22×Q16—861no—
302C22×SD16—21no—
303#539—434no—
304#539—862no—
305#539—862no—
306#539—862no—
307C2×#126—861no—
308C2×#125—861no—
309C2×#123—861no—
310C2×#123—861no—
311C2×C22⋊Q8—431no—
312C2×C22⋊Q8—861no—
313C2×#121C2×D4311yescharacteristic
314C2×C4×D4—861no—
315C22×C4⋊C4—431no—
316C22×C4⋊C4—861no—
317#451—434no—
318#451—862no—
319#448—22no—
320#448C2×D4314yes—
321C2×#103—21no—
322C2×#103—861no—
323C2×C22⋊C8—431no—
324C2×C22⋊C8C2×D4311yescharacteristic
325#395—434no—
326#395—862no—
327C2×#95—431no—
328C2×#95—861no—
329#328—434no—
330#327—434no—
331#324—434no—
332C43C2×#160311yescharacteristic, complemented, Sylow
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—44no—
339C22×Q8—431no—
340C22×Q8C22×D4312yes—
341C22×D4—21no—
342C22×D4C22⋊D4311yescharacteristic
343C23×C4—21no—
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—861no—
347C23×C4—861no—
348C23×C4C22×D4311yescharacteristic
349C2×Q16—864no—
350C2×Q16—1724no—
351C2×SD16—24no—
352C2×SD16—44no—
353C22×C8—21no—
354C22×C8—861no—
355#126—864no—
356#126—864no—
357#125—864no—
358#125—864no—
359#123—864no—
360#123—864no—
361#123—864no—
362#123—864no—
363C22⋊Q8—432no—
364C22⋊Q8—432no—
365C22⋊Q8—864no—
366C22⋊Q8—864no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369#121—21no—
370#121—21no—
371#121C22⋊D4312yes—
372#121C22×D4312yes—
373C4×D4—864no—
374C4×D4—864no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—432no—
377C2×C4⋊C4—432no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—864no—
387C2×C4⋊C4—1724no—
388C2×C4⋊C4C22⋊D4311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C42—861no—
395#103—24no—
396#103—864no—
397C22⋊C8—21no—
398C22⋊C8—432no—
399C22⋊C8—861no—
400C22⋊C8C22×D4312yes—
401#95—432no—
402#95—864no—
403#95—861no—
404C24—21no—
405C24D4×D4311yescharacteristic
406C2×Q8—24no—
407C2×Q8—24no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—44no—
411C2×Q8—42no—
412C2×Q8—42no—
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—432no—
419C2×Q8—861no—
420C2×Q8—1722no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C2×C22⋊D4312yes—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—864no—
438C22×C4—861no—
439C22×C4—864no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—3442no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458Q16—1728no—
459SD16—48no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—862no—
463C2×C8—1722no—
464C4⋊C4—21no—
465C4⋊C4—432no—
466C4⋊C4—864no—
467C4⋊C4—864no—
468C4⋊C4—864no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C4⋊C4—861no—
472C4⋊C4—862no—
473C4⋊C4—862no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—1728no—
477C4⋊C4C2×C22⋊D4312yes—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—864no—
481C22⋊C4—864no—
482C22⋊C4—864no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C42—864no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23#1306329311yescharacteristic
493C23#1306329311yescharacteristic
494C23#1306334612yes—
495C23#1306335412yes—
496C23C2×D4×D4311yescharacteristic
497Q8—24no—
498Q8—24no—
499Q8—42no—
500Q8—42no—
501Q8—44no—
502Q8—44no—
503Q8—3441no—
504Q8—1722no—
505D4—42no—
506D4—44no—
507D4—42no—
508D4—42no—
509D4—81no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—864no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—3441no—
531C2×C4—3444no—
532C2×C4—1722no—
533C2×C4—1728no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4#1306329311yescharacteristic
542C2×C4#1306329311yescharacteristic
543C2×C4C2×D4×D4311yescharacteristic
544C2×C4C22×C22⋊D4311yescharacteristic
545C8—42no—
546C8—1722no—
547C22—21no—
548C22—21no—
549C22—24no—
550C22—24no—
551C22—21no—
552C22—21no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—84no—
557C22#1458305812yes—
558C22#1458305812yes—
559C22#1458308012yes—
560C22#1458308512yes—
561C22C2×#1306329311yescharacteristic
562C22C2×#1306334611yescharacteristic
563C22C2×#1306335411yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—44no—
569C4—42no—
570C4—1724no—
571C4—1722no—
572C4—1722no—
573C4—1722no—
574C4—1722no—
575C2—21no—
576C2—22no—
577C2—21no—
578C2—82no—
579C2#1913355514yesdirect product factor
580C2C2×#1458305811yescharacteristic
581C2C2×#1458308011yescharacteristic
582C2C2×#1458308511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#448C2
socleC23×C43#120
prime radicalC2×#121×C43C22
hypercenterC2×#448D43
hypocenterC43C2×#1603
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14583055C2semidirect
3. C2×#14582818C2semidirect
4. #19133555C2direct (N × H)
5. C2×#14582637C2semidirect
7. C2×#14582624C2semidirect
24. #14583055C22semidirect
28. #14582818C22semidirect
31. #14582637C22semidirect
33. #14582624C22semidirect
296. C2×C43#1603semidirect
332. C43C2×#1603semidirect
579. C2#19133555direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145834942
C2×#145830552
C2×#145828182
#191335552
C2×#145826372
C2×#145826332
C2×#145826242
C2×C43×#4482
C2×#160343